ps6 - Problem Set#6 IE 316 Due 1 2 3 4 5.1 5.4 5.7 The...

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Problem Set #6 IE 316 Due October 29, 2001 1. 5.1 2. 5.4 3. 5.7 4. The output of a paper mill consists of standard rolls 110 inches (110") wide, which are cut into smaller rolls to meet orders. This week, there are orders for smaller rolls of the following widths: Width Orders 20" 48 45" 35 50" 24 55" 10 75" 8 The owner of the mill wants to know what cutting patterns to apply so as to fill the orders using the smallest number of 110" rolls. A cutting pattern consists of a certain number of smaller rolls of each width that can be cut from one larger roll, such as two of 45" and one of 20", or one of 50" and one of 55" (and 5" of waste). Notice that the sum of the widths of the smaller rolls in the pattern must be less than 110". For example, we could consider the following six patterns: Width 1 2 3 4 5 6 20" 3 1 0 2 1 3 45" 0 2 0 0 0 1 50" 1 0 1 0 0 0 55" 0 0 1 1 0 0 75" 0 0 0 0 1 0 The pattern in the first column represents 3 20" rolls and one 50" roll. a. Develop an AMPL model, allowing for any set of order widths and any set of patterns, that minimizes the total number of 110" rolls used, assuming that the number of smaller rolls produced need only be greater than or equal to the number

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